Multiply the following complex numbers: $({-3-2i}) \cdot ({-4+3i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-2i}) \cdot ({-4+3i}) = $ $ ({-3} \cdot {-4}) + ({-3} \cdot {3}i) + ({-2}i \cdot {-4}) + ({-2}i \cdot {3}i) $ Then simplify the terms: $ (12) + (-9i) + (8i) + (-6 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 12 + (-9 + 8)i - 6i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 12 + (-9 + 8)i - (-6) $ The result is simplified: $ (12 + 6) + (-1i) = 18-i $